This notebook will begin looking at clustering methods on the expression of the genes in a single sample of the dataset of interest, from an unbiased approach.

Set Up

# Load libraries
library(magrittr)
library(scater)
library(readr)
library(bluster)
library(ggpubr)
library(pheatmap)

# Set file paths
data_dir <- file.path("results", "Gawad_processed_data")

# Source custom functions script
source(file.path("utils", "clustering-functions.R"))

Read in data

sample_290_normalized <- read_rds(
  file.path(data_dir, "SCPCS000216", "SCPCL000290_miQC_downstream_processed_normalized_reduced_sce.rds"))

Perform clustering

k-means

# Perform k-means clustering
kmeans_cluster_names <- paste0("kcluster", c(2:15))

sample_290_normalized <- kmeans_clustering(
  sample_290_normalized,
  k_range = c(2:15),
  check_stability = TRUE
)

# Plot k-means
kmeans_plot_list <- kmeans_cluster_names %>%
  purrr::map(~ plotReducedDim(sample_290_normalized, dimred = "UMAP", colour_by = .x))

cowplot::plot_grid(plotlist = kmeans_plot_list, ncol = 4)

graph-based, walktrap

# Perform graph-based walktrap clustering
walktrap_cluster_names <-paste0("walktrap_cluster", c(5, 10, 15, 20, 25, 50, 100))

sample_290_normalized <- graph_clustering(
  sample_290_normalized,
  nn_range = c(5, 10, 15, 20, 25, 50, 100),
  weighting_type = "rank",
  cluster_function = "walktrap",
  check_stability = TRUE
)
detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'
# Plot
walktrap_plot_list <- walktrap_cluster_names %>%
   purrr::map(~ plotReducedDim(sample_290_normalized, dimred = "UMAP", colour_by = .x))

cowplot::plot_grid(plotlist = walktrap_plot_list, ncol = 3)

graph-based, louvain

# Perform graph-based louvain clustering
louvain_cluster_names <- paste0("louvain_cluster", c(5, 10, 15, 20, 25, 50, 100))

sample_290_normalized <- graph_clustering(
  sample_290_normalized,
  nn_range = c(5, 10, 15, 20, 25, 50, 100),
  weighting_type = "jaccard",
  cluster_function = "louvain",
  check_stability = TRUE
)
detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'detected tied distances to neighbors, see ?'BiocNeighbors-ties'
# Plot
louvain_plot_list <- louvain_cluster_names %>%
   purrr::map(~ plotReducedDim(sample_290_normalized, dimred = "UMAP", colour_by = .x))


cowplot::plot_grid(plotlist = louvain_plot_list, ncol = 3)

Check cluster validity stats

k-means

# Check the k-means cluster validity stats for each of the clusters and produce
# a summary data frame of these stats to be stored within the SCE object
sample_290_normalized <- add_metadata_clustering_stats(sample_290_normalized, kmeans_cluster_names, "kmeans")
Joining, by = "cell_barcode"
Joining, by = "cell_barcode"
Joining, by = "cell_barcode"
Joining, by = "cell_barcode"
Joining, by = "cell_barcode"
Joining, by = "cell_barcode"
Joining, by = "cell_barcode"
Joining, by = "cell_barcode"
Joining, by = "cell_barcode"
Joining, by = "cell_barcode"
Joining, by = "cell_barcode"
Joining, by = "cell_barcode"
Joining, by = "cell_barcode"
Joining, by = "cell_barcode"
# Preview the saved results
head(metadata(sample_290_normalized)$all_stats$kmeans)

# Preview the saved summary results
head(metadata(sample_290_normalized)$summary_stats$kmeans)

purity plots

# Plot individual cluster and summary stats
kmeans_plots <- plot_clustering_validity(metadata(sample_290_normalized)$all_stats$kmeans,
                         metadata(sample_290_normalized)$summary_stats$kmeans,
                         "purity", "maximum", "cluster_names", c(2:15))
Outer names are only allowed for unnamed scalar atomic inputs
kmeans_plots

silhouette width plots

# Plot individual cluster and summary stats
kmeans_silhouette_plots <- plot_clustering_validity(metadata(sample_290_normalized)$all_stats$kmeans,
                         metadata(sample_290_normalized)$summary_stats$kmeans,
                         "width", "closest", "cluster_names", c(2:15))
Outer names are only allowed for unnamed scalar atomic inputs
kmeans_silhouette_plots

graph-based, walktrap

# Check the walktrap cluster validity stats for each of the clusters and produce
# a summary data frame of these stats to be stored within the SCE object
sample_290_normalized <- add_metadata_clustering_stats(sample_290_normalized, walktrap_cluster_names, "walktrap")
Joining, by = "cell_barcode"
Joining, by = "cell_barcode"
Joining, by = "cell_barcode"
Joining, by = "cell_barcode"
Joining, by = "cell_barcode"
Joining, by = "cell_barcode"
Joining, by = "cell_barcode"
  
# Preview the saved results
head(metadata(sample_290_normalized)$all_stats$walktrap)

# Preview the saved summary results
head(metadata(sample_290_normalized)$summary_stats$walktrap)

purity plots

# Plot individual cluster and summary stats
walktrap_plots <- plot_clustering_validity(metadata(sample_290_normalized)$all_stats$walktrap,
                         metadata(sample_290_normalized)$summary_stats$walktrap,
                         "purity", "maximum", "cluster_names", c(5, 10, 15, 20, 25, 50, 100))
Outer names are only allowed for unnamed scalar atomic inputs
walktrap_plots

silhouette width plots

# Plot individual cluster and summary stats
walktrap_silhouette_plots <- plot_clustering_validity(metadata(sample_290_normalized)$all_stats$walktrap,
                         metadata(sample_290_normalized)$summary_stats$walktrap,
                         "width", "closest", "cluster_names", c(5, 10, 15, 20, 25, 50, 100))
Outer names are only allowed for unnamed scalar atomic inputs
walktrap_silhouette_plots

graph-based, louvain

# Check the louvain cluster validity stats for each of the clusters and produce
# a summary data frame of these stats to be stored within the SCE object
sample_290_normalized <- add_metadata_clustering_stats(sample_290_normalized, louvain_cluster_names, "louvain")
Joining, by = "cell_barcode"
Joining, by = "cell_barcode"
Joining, by = "cell_barcode"
Joining, by = "cell_barcode"
Joining, by = "cell_barcode"
Joining, by = "cell_barcode"
Joining, by = "cell_barcode"
# Preview the saved results
head(metadata(sample_290_normalized)$all_stats$louvain)

# Preview the saved summary results
head(metadata(sample_290_normalized)$summary_stats$louvain)

purity plots

# Plot individual cluster and summary stats
louvain_plots <- plot_clustering_validity(metadata(sample_290_normalized)$all_stats$louvain,
                         metadata(sample_290_normalized)$summary_stats$louvain,
                         "purity", "maximum", "cluster_names", c(5, 10, 15, 20, 25, 50, 100))
Outer names are only allowed for unnamed scalar atomic inputs
louvain_plots

silhouette width plots

# Plot individual cluster and summary stats
louvain_silhouette_plots <- plot_clustering_validity(metadata(sample_290_normalized)$all_stats$louvain,
                         metadata(sample_290_normalized)$summary_stats$louvain,
                         "width", "closest", "cluster_names", c(5, 10, 15, 20, 25, 50, 100))
Outer names are only allowed for unnamed scalar atomic inputs
louvain_silhouette_plots

Check cluster stability

k-means

# Check and plot cluster stability
kmeans_cluster_names %>%
  purrr::walk(~ plot_cluster_stability(sample_290_normalized, .x))

graph-based, walktrap

walktrap_cluster_names %>%
  purrr::walk(~ plot_cluster_stability(sample_290_normalized, .x))

graph-based, louvain

louvain_cluster_names %>%
  purrr::walk(~ plot_cluster_stability(sample_290_normalized, .x))

Session info

sessionInfo()
R version 4.1.2 (2021-11-01)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 18.04.3 LTS

Matrix products: default
BLAS:   /usr/lib/x86_64-linux-gnu/openblas/libblas.so.3
LAPACK: /usr/lib/x86_64-linux-gnu/libopenblasp-r0.2.20.so

locale:
 [1] LC_CTYPE=C.UTF-8       LC_NUMERIC=C           LC_TIME=C.UTF-8        LC_COLLATE=C.UTF-8    
 [5] LC_MONETARY=C.UTF-8    LC_MESSAGES=C.UTF-8    LC_PAPER=C.UTF-8       LC_NAME=C             
 [9] LC_ADDRESS=C           LC_TELEPHONE=C         LC_MEASUREMENT=C.UTF-8 LC_IDENTIFICATION=C   

attached base packages:
[1] grid      stats4    stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] pheatmap_1.0.12             ggpubr_0.4.0                bluster_1.4.0              
 [4] HDF5Array_1.22.1            rhdf5_2.38.0                DelayedArray_0.20.0        
 [7] Matrix_1.3-4                ComplexHeatmap_2.10.0       scater_1.22.0              
[10] ggplot2_3.3.5               scuttle_1.4.0               SingleCellExperiment_1.16.0
[13] SummarizedExperiment_1.24.0 Biobase_2.54.0              GenomicRanges_1.46.1       
[16] GenomeInfoDb_1.30.0         IRanges_2.28.0              S4Vectors_0.32.3           
[19] BiocGenerics_0.40.0         MatrixGenerics_1.6.0        matrixStats_0.61.0         
[22] readr_2.1.1                 magrittr_2.0.1             

loaded via a namespace (and not attached):
 [1] ggbeeswarm_0.6.0          colorspace_2.0-2          ggsignif_0.6.3            rjson_0.2.20             
 [5] ellipsis_0.3.2            modeltools_0.2-23         circlize_0.4.13           XVector_0.34.0           
 [9] GlobalOptions_0.1.2       BiocNeighbors_1.12.0      rstudioapi_0.13           clue_0.3-60              
[13] farver_2.1.0              ggrepel_0.9.1             flexmix_2.3-17            fansi_0.5.0              
[17] codetools_0.2-18          splines_4.1.2             sparseMatrixStats_1.6.0   doParallel_1.0.16        
[21] knitr_1.36                polyclip_1.10-0           broom_0.7.10              cluster_2.1.2            
[25] png_0.1-7                 ggforce_0.3.3             compiler_4.1.2            backports_1.4.0          
[29] assertthat_0.2.1          fastmap_1.1.0             cli_3.1.0                 tweenr_1.0.2             
[33] BiocSingular_1.10.0       miQC_1.2.0                htmltools_0.5.2           tools_4.1.2              
[37] rsvd_1.0.5                igraph_1.2.9              gtable_0.3.0              glue_1.5.1               
[41] GenomeInfoDbData_1.2.7    dplyr_1.0.7               Rcpp_1.0.7                carData_3.0-4            
[45] vctrs_0.3.8               rhdf5filters_1.6.0        iterators_1.0.13          DelayedMatrixStats_1.16.0
[49] xfun_0.28                 beachmat_2.10.0           lifecycle_1.0.1           irlba_2.3.3              
[53] renv_0.14.0               rstatix_0.7.0             zlibbioc_1.40.0           MASS_7.3-54              
[57] scales_1.1.1              hms_1.1.1                 parallel_4.1.2            RColorBrewer_1.1-2       
[61] yaml_2.2.1                gridExtra_2.3             foreach_1.5.1             ScaledMatrix_1.2.0       
[65] BiocParallel_1.28.2       shape_1.4.6               rlang_0.4.12              pkgconfig_2.0.3          
[69] bitops_1.0-7              evaluate_0.14             lattice_0.20-45           purrr_0.3.4              
[73] Rhdf5lib_1.16.0           labeling_0.4.2            cowplot_1.1.1             tidyselect_1.1.1         
[77] R6_2.5.1                  generics_0.1.1            DBI_1.1.1                 pillar_1.6.4             
[81] withr_2.4.3               abind_1.4-5               RCurl_1.98-1.5            nnet_7.3-16              
[85] tibble_3.1.6              crayon_1.4.2              car_3.0-12                utf8_1.2.2               
[89] tzdb_0.2.0                rmarkdown_2.11            viridis_0.6.2             GetoptLong_1.0.5         
[93] data.table_1.14.2         digest_0.6.29             tidyr_1.1.4               munsell_0.5.0            
[97] beeswarm_0.4.0            viridisLite_0.4.0         vipor_0.4.5              
---
title: "Clustering"
author: Data Lab for ALSF
date: 2022
output:
  html_notebook: 
    toc: true
    toc_float: true
---

This notebook will begin looking at clustering methods on the expression of the genes in a single sample of the dataset of interest, from an unbiased approach.

## Set Up 

```{r}
# Load libraries
library(magrittr)
library(scater)
library(readr)
library(bluster)
library(ggpubr)
library(pheatmap)

# Set file paths
data_dir <- file.path("results", "Gawad_processed_data")

# Source custom functions script
source(file.path("utils", "clustering-functions.R"))
```

## Read in data

```{r}
sample_290_normalized <- read_rds(
  file.path(data_dir, "SCPCS000216", "SCPCL000290_miQC_downstream_processed_normalized_reduced_sce.rds"))
```

## Perform clustering

### k-means

```{r fig.height = 10.5}
# Perform k-means clustering
kmeans_cluster_names <- paste0("kcluster", c(2:15))

sample_290_normalized <- kmeans_clustering(
  sample_290_normalized,
  k_range = c(2:15),
  check_stability = TRUE
)

# Plot k-means
kmeans_plot_list <- kmeans_cluster_names %>%
  purrr::map(~ plotReducedDim(sample_290_normalized, dimred = "UMAP", colour_by = .x))

cowplot::plot_grid(plotlist = kmeans_plot_list, ncol = 4)
```

### graph-based, walktrap

```{r fig.height = 9.5}
# Perform graph-based walktrap clustering
walktrap_cluster_names <-paste0("walktrap_cluster", c(5, 10, 15, 20, 25, 50, 100))

sample_290_normalized <- graph_clustering(
  sample_290_normalized,
  nn_range = c(5, 10, 15, 20, 25, 50, 100),
  weighting_type = "rank",
  cluster_function = "walktrap",
  check_stability = TRUE
)

# Plot
walktrap_plot_list <- walktrap_cluster_names %>%
   purrr::map(~ plotReducedDim(sample_290_normalized, dimred = "UMAP", colour_by = .x))

cowplot::plot_grid(plotlist = walktrap_plot_list, ncol = 3)
```

### graph-based, louvain

```{r fig.height = 8.5}
# Perform graph-based louvain clustering
louvain_cluster_names <- paste0("louvain_cluster", c(5, 10, 15, 20, 25, 50, 100))

sample_290_normalized <- graph_clustering(
  sample_290_normalized,
  nn_range = c(5, 10, 15, 20, 25, 50, 100),
  weighting_type = "jaccard",
  cluster_function = "louvain",
  check_stability = TRUE
)

# Plot
louvain_plot_list <- louvain_cluster_names %>%
   purrr::map(~ plotReducedDim(sample_290_normalized, dimred = "UMAP", colour_by = .x))


cowplot::plot_grid(plotlist = louvain_plot_list, ncol = 3)
```

## Check cluster validity stats

### k-means

```{r fig.height = 20.5}
# Check the k-means cluster validity stats for each of the clusters and produce
# a summary data frame of these stats to be stored within the SCE object
sample_290_normalized <- add_metadata_clustering_stats(sample_290_normalized, kmeans_cluster_names, "kmeans")

# Preview the saved results
head(metadata(sample_290_normalized)$all_stats$kmeans)

# Preview the saved summary results
head(metadata(sample_290_normalized)$summary_stats$kmeans)
```
#### purity plots

```{r fig.height=10, fig.width=15}
# Plot individual cluster and summary stats
kmeans_plots <- plot_clustering_validity(metadata(sample_290_normalized)$all_stats$kmeans,
                         metadata(sample_290_normalized)$summary_stats$kmeans,
                         "purity", "maximum", "cluster_names", c(2:15))
kmeans_plots
```

#### silhouette width plots

```{r fig.height=10, fig.width=15}
# Plot individual cluster and summary stats
kmeans_silhouette_plots <- plot_clustering_validity(metadata(sample_290_normalized)$all_stats$kmeans,
                         metadata(sample_290_normalized)$summary_stats$kmeans,
                         "width", "closest", "cluster_names", c(2:15))
kmeans_silhouette_plots
```

### graph-based, walktrap

```{r fig.height = 15.5}
# Check the walktrap cluster validity stats for each of the clusters and produce
# a summary data frame of these stats to be stored within the SCE object
sample_290_normalized <- add_metadata_clustering_stats(sample_290_normalized, walktrap_cluster_names, "walktrap")
  
# Preview the saved results
head(metadata(sample_290_normalized)$all_stats$walktrap)

# Preview the saved summary results
head(metadata(sample_290_normalized)$summary_stats$walktrap)
```
#### purity plots

```{r fig.height=10, fig.width=15}
# Plot individual cluster and summary stats
walktrap_plots <- plot_clustering_validity(metadata(sample_290_normalized)$all_stats$walktrap,
                         metadata(sample_290_normalized)$summary_stats$walktrap,
                         "purity", "maximum", "cluster_names", c(5, 10, 15, 20, 25, 50, 100))
walktrap_plots
```

#### silhouette width plots

```{r fig.height=10, fig.width=15}
# Plot individual cluster and summary stats
walktrap_silhouette_plots <- plot_clustering_validity(metadata(sample_290_normalized)$all_stats$walktrap,
                         metadata(sample_290_normalized)$summary_stats$walktrap,
                         "width", "closest", "cluster_names", c(5, 10, 15, 20, 25, 50, 100))
walktrap_silhouette_plots
```

### graph-based, louvain

```{r fig.height = 9.5}
# Check the louvain cluster validity stats for each of the clusters and produce
# a summary data frame of these stats to be stored within the SCE object
sample_290_normalized <- add_metadata_clustering_stats(sample_290_normalized, louvain_cluster_names, "louvain")

# Preview the saved results
head(metadata(sample_290_normalized)$all_stats$louvain)

# Preview the saved summary results
head(metadata(sample_290_normalized)$summary_stats$louvain)
```
#### purity plots

```{r fig.height=10}
# Plot individual cluster and summary stats
louvain_plots <- plot_clustering_validity(metadata(sample_290_normalized)$all_stats$louvain,
                         metadata(sample_290_normalized)$summary_stats$louvain,
                         "purity", "maximum", "cluster_names", c(5, 10, 15, 20, 25, 50, 100))
louvain_plots
```

#### silhouette width plots

```{r fig.height=10}
# Plot individual cluster and summary stats
louvain_silhouette_plots <- plot_clustering_validity(metadata(sample_290_normalized)$all_stats$louvain,
                         metadata(sample_290_normalized)$summary_stats$louvain,
                         "width", "closest", "cluster_names", c(5, 10, 15, 20, 25, 50, 100))
louvain_silhouette_plots
```

## Check cluster stability

### k-means

```{r}
# Check and plot cluster stability
kmeans_cluster_names %>%
  purrr::walk(~ plot_cluster_stability(sample_290_normalized, .x))
```

### graph-based, walktrap

```{r}
walktrap_cluster_names %>%
  purrr::walk(~ plot_cluster_stability(sample_290_normalized, .x))
```

### graph-based, louvain

```{r}
louvain_cluster_names %>%
  purrr::walk(~ plot_cluster_stability(sample_290_normalized, .x))
```

## Session info

```{r}
sessionInfo()
```
